Put every connection on a Tab

At the right side we see the open connection among each other. It is difficult to see which connection you are working with.
If each connection is on its own tab, you can switch between the connections more easily, and it remains clear which connection you are working on.

Ok, that's the approach HeidiSQL is using now since several years. A tab interface involves a lot changes to the whole UI.

and it remains clear which connection you are working on

There are more aspects in that idea than this.

The current UI is intentionally one tree, so users still are able to see all connections at least with a part of their databases. That's a benefit when you're working on similar systems, like a dev server and live server.

For a better separation between different connections, I had introduced session background colors (like that light blue in the attached screenshot). Also, the focused connection nodes are painted in normal text color, while the other ones are dimmed to a grey.

Several years ago (must have been up to v3.1, see https://sourceforge.net/p/heidisql/tickets/365/ ), HeidiSQL had a multi-document-interface (MDI), which was horrible. Users complained about having to resize controls for each connection. There was then my idea to support multiple connections in one tree, which helped a lot. Just being a bit nostalgic...